The European Commission, the executive arm of the European Union, plans to give the European Central Bank oversight of all banks in the euro zone, German paper Sueddeutsche Zeitung reported, citing EU Commissioner Michel Barnier.

Under the plans, the ECB will oversee all banks that have tapped the European Stability Mechanism from January next year, all banks relevant to the financial system from July and all remaining banks from 2014, Barnier told the paper in an interview.

Countries outside the euro zone can subject their banks to the oversight of the ECB voluntarily, said the commissioner, according to Sueddeutsche.

The plans are in line with demands from the Austrian financial regulator, who said on Thursday that the ECB should take charge not only of banks considered vital for the banking system.

European Union leaders agreed in June to set up a single banking supervisor for Europe centred around the ECB, a plan they hope will help break the "vicious" link between the euro zone's debt crisis and struggling banks.

The European Commission will present a detailed proposal on September 12 for that supervisor.

Details have yet to be agreed about how the ECB will work with local regulators in individual countries and with the existing European Banking Authority, the pan-EU watchdog.

(Reporting by Peter Dinkloh; Editing by Hugh Lawson)